The feasible region of an LPP is shown in the figure. If \( z=3 x+9 y \), then the minimum value of
z occurs at

• Correct answer
  A

  \( (5,5) \)
• B

  \( (0,10) \)
• C

  \( (0,20) \)
• D

  \((15,15) \)

Solution

Given that, \( z=3 x+9 y \)

The least point is \( (5,5) \)
\[ \begin{array}{l} \text { So, } z(5,5)=3(5)+9(5) \\ =15+45=60 \end{array} \]
Now take point \( (0,10) \).
So, \( z(0,10)=3(0)+9(10)=90 \)
Therefore, minimum value of \( z \) is at \( (5,5) \)

Hence, the correct answer is option: 'A'.